64 Is Not The Answer!

Algebra Level 5

\[\big(x^3+y^3\big)\big(y^3+z^3\big)\big(z^3+x^3\big) \le k(x+y)(y+z)(z+x)\]

Find the minimum value of \(k\) such that for all non-negative reals with satisfy \( x + y + z = 6 \), the above inequality is true.

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