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

Find the sum of all $x$ that satisfy the equation above.

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