# Adding another reciprocal

Algebra Level 4

Given that $$xyz=1$$ where $$x,y,z$$ are positive real numbers and that $$x+\dfrac{1}{z}=5$$, $$y+\dfrac{1}{x}=29$$ and $$z+\dfrac{1}{y}=\dfrac{m}{n}$$, where $$m$$ and $$n$$ are coprime positive integers. Compute $$m+n$$.

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