World Tour Poland 06

Algebra Level 4

Let \(x\), \(y\) and \(z\) be the real solutions of the system

\(x^{5}=5y^{3}-4z\)

\(y^{5}=5z^{3}-4x\)

\(z^{5}=5x^{3}-4y\)

Submit your answer as the maximum value of \(x+y+z\).

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