Find the sum of all the integers \(x, y, z\) satisfying the inequality \( x \leq y \leq z \) and the equation:

\[ (x^3)(y^3 + z^3) = 2012(xyz + 2). \]

Note: Credits to International Mathematical Olympiad. Provide simple solution, I'll try to understand the solution given on the website but try also different ways. Good luck!

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