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Possible value(s)

Algebra Level 4

Let $x , y$ and $z$ be distinct nonzero numbers such that $\frac{x^3 +1}{x}=\frac{y^3+1}{y}=\frac{z^3+1}{z}.$

What is the value of $x^3+y^3+z^3?$

-1 -4 4 1 3 -3

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by Hana Wehbi

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