Alternating sum of sum of powers?

If $n$ is a positive integer with a unit digit of $5$ . Denote $N$ as the alternating sum of $( 12^n + 9^n + 8^n + 6^n)$ . What is the sum of all possible values of $M = N \bmod {11}$ ?

Details and assumptions : As an explicit example, the alternating sum of $43576 = 4 - 3 + 5 - 7 + 6 = 5$