Minimum value, you say?

Algebra Level 3

\[\large \frac{x^6}{y^3 + z^3} + \frac{y^6}{z^3 + x^3} + \frac{z^6}{x^3 + y^3}\]

Let \(x\), \(y\) and \(z\) be three positive real numbers satisfying \(xyz=2\). Find the minimum value of the expression above.

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