Possible value(s)

Algebra Level 4

Let x,yx , y and zz be distinct nonzero numbers such that x3+1x=y3+1y=z3+1z.\frac{x^3 +1}{x}=\frac{y^3+1}{y}=\frac{z^3+1}{z}.

What is the value of x3+y3+z3?x^3+y^3+z^3?

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