# Triple System of Equations

Algebra Level 4

\large \begin{align*}\alpha+\beta+\gamma&=6 \\\alpha^3+\beta^3+\gamma^3&=87\\ (\alpha+1)(\beta+1)(\gamma+1)&=33 \end{align*}

Suppose $$\alpha$$, $$\beta$$, and $$\gamma$$ are complex numbers that satisfy the system of equations above.

If $$\frac1\alpha+\frac1\beta+\frac1\gamma=\tfrac mn$$ for positive coprime integers $$m$$ and $$n$$, find $$m+n$$.

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