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Let x,yx , y x,y and zzz 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}.xx3+1=yy3+1=zz3+1.
What is the value of x3+y3+z3?x^3+y^3+z^3?x3+y3+z3?
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