# Polynomial Again?

Algebra Level 5

$\begin{cases} x^3-xyz=2 \\ y^3-xyz =6 \\ z^3-xyz = 20 \end{cases}$

If $$x,y$$ and $$z$$ are real solutions satisfying the system of equations above, and the maximum value of $$x^3+y^3+z^3$$ is equal to $$\dfrac mn$$, where $$m$$ and $$n$$ are coprime positive integers, find $$m+n$$.

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