Ken's POTW

Alternative Dice
A regular pair of dice consists of two 6-sided dice with the numbers 1 through 6 on both dice, yielding the following probability for each sum:
2:1/36 3:2/36 4:3/36 5:4/36 6:5/36 7:6/36
8:5/36 9:4/36 10:3/36 11:2/36 12:1/36
Can you find other sets of dice that yield this same probability table?

Source: Original, based upon a puzzle from Ken Burres' Math Problem of the Week.

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