Easy Algebra Manipulation

Algebra Level 2

(x+1)5+(x+1)4(x1)+(x+1)3(x1)2+(x+1)2(x1)3+(x+1)(x1)4+(x1)5=0\begin{aligned} && (x+1)^5+(x+1)^4(x-1)+(x+1)^3(x-1)^2 \\ &+& (x+1)^2(x-1)^3+(x+1)(x-1)^4+(x-1)^5=0 \end{aligned}

Find the sum of all xx that satisfy the equation above.

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