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

(x3)(y3+z3)=2012(xyz+2). (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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