Determine the sum of the squares of all **real** numbers \(x\) that satisfy the equation

\[[(x+1)^2-x][(x+1)^2][(x+1)^2 +2x] = -2x^5 + 4x^3 -2x\]

Note:

Only count repeated roots once.

Please

**do not**use WolframAlpha.

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