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Algebra Level 5

\[\begin{eqnarray} &\left[(x^2+x+1)^3-(x^2+1)^3-x^3\right] \left[(x^2-x+1)^3-(x^2+1)^3+x^3\right]& \\ &= & \\ &3 \left[(x^4+x^2+1)^3-(x^4+1)^3-x^6\right] &\end{eqnarray} \]

Find the sum of all the integral values of \(x\) which satisfy the equation above.

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