Quote:
Originally Posted by Skammer
...
Since we are told that the pair contains at least one six, we have 11 possible combinations with equal chance of occurring. ...

IMO the above part is right. Then you go wrong here:
Quote:
Originally Posted by Skammer
... If a six is then removed, only 1 of the remaining 11 dice is another six. So I maintain the answer is 1/11.
...

How many different ways can we remove a six? Let's assume we have a green and a red die so we can tell them apart. As you said, the possibilities expressed in green, red order are:
1,6
2,6
3,6
4,6
5,6
6,6
6,5
6,4
6,3
6,2
6,1
If the green die is a 6 we're looking at one of the bottom 6 possibilities. 1/6th of which have another 6, the red die.
If the red die is a 6 we're looking at one of the top 6 possibilities. 1/6th of which have another 6, the green die.
Result: it doesn't matter which die is a 6. Red, green, or both. After you remove one of the sixes the chance of the other being a 6 is 1/6.