Reverse Fractions

Algebra Level 3

Let \[\dfrac{x}{y}+\dfrac{y}{z}+\dfrac{z}{x}=-2 \quad \text{ and } \quad \dfrac{y}{x}+\dfrac{z}{y}+\dfrac{x}{z}=0.\]

If \(M = \dfrac{x^{3}}{y^{3}}+\dfrac{y^{3}}{z^{3}}+\dfrac{z^{3}}{x^{3}},\) then find the value of \(M.\)

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