Rarity:
Unique

Known examples:
1. PCGS MS-66 Red.  Found in a bank-wrapped roll of pennies by an anonymous collector sometime before December 1999, then sold to Jack Dempsey of Dempsey & Baxter for an undisclosed sum, who displayed the mule at the 2001 Florida United Numismatists Convention (it was not for sale at that time).

Images courtesy of Dempsey & Baxter

The following information was provided by Jack Dempsey of Dempsey & Baxter:

Background:
This coin was stuck at the Philadelphia Mint in 1999. The coin is a normal cent planchet, comprised of copper-plated zinc, weighing approximately 2.5 grams. The coin was stuck with an Obverse Lincoln cent die and a reverse Roosevelt dime die. Prior to 1999, this type of a strike wasn't possible without some kind of tampering with the coining presses and dies at The Mint. The Mint has not released an official statement on this coin, so we can only arrive at two scenarios by which it could have been manufactured and reached circulation

The year 1999 brought with it a new era in Coin Manufacturing in the United States. The Mint, while faced with a Cent shortage, needed to crank out billions of Statehood Quarters. This, along with anticipated demand for the Sacagawea Dollars to be released in 2000, prompted some changes at the Mint facility in Philadelphia. High-Speed Schueller presses were installed to manufacture Statehood Quarters for circulation. Our first guess is that while these new presses were being tested, some trial strikes were manufactured. It is likely that this coin escaped in a tote bin after a series of trial strikes were run. The similar size of the coins, as well as universally fitting dies and die hubs on the new presses make this a very likely possibility

Another possible scenario is the factor of simple human error. It is very possible that a high speed press was being used to strike pennies when a problem occured with the reverse die. When the die was exchanged at the die vault, the die technician didn't realize he had been given a reverse dime die. When the mistake was discovered, at least one of these 11-Cent Mules escaped the scrap bin

It remains to be seen whether this piece is unique. With all the publicity surrounding the Sacagawea Quarter-Dollar Mules earlier this year, we thought surely another 11-Cent Mule would surface. To our knowledge, this is the only example, but the hunt for another continues. It's more than likely further specimens, if found, would be circulated due to the amount of time that has passed since the 11-Cent mule's manufacture. The coin is graded MS-66 Red by the Professional Coin Grading Service (PCGS).

Obverse:
The obverse shows details of a normal 1999 Cent, except that the "L" in Liberty is obliterated due to the difference in sizes of cent and dime dies. The "i" in Liberty, Lincoln's shoulder, and "In God We Trust" also show considerable flatness due to this die size difference. All other details show normally. The ear shows full detail and there is a small amount of finger smudge in the fields from handling.

Reverse:
The reverse side of the coin is that of a Roosevelt dime. The strike is slightly off-center, with all details showing. The dime "rim" is present all the way around the coin. The reverse is struck about 15-20% rotated. Some photos make the reverse appear slightly clad colored; the reverse is a full bright red, with original mint luster.

Sources and/or recommended reading: