Alternating sum of sum of powers?

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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 \(43576 = 4 - 3 + 5 - 7 + 6 = 5 \)

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