Out of Nowhere?

\[ 9^n + 28^n + 33^n + 71^n + 76^n + 95^n = A^n + B^n + C^n + D^n + E^n + F^n \]

The equation above holds true for \(n = 0, 1, 2, 3, 4, 5 \) and distinct integers \(A\), \(B\), \(C\), \(D\), \(E\), and \(F\) that are different from any of the permutations of those on the LHS.

Find \(A\times B\times C \times D \times E \times F\). You may use a calculator for the final step of your computation.

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