# Another AIME problem

Algebra Level 3

$\begin{cases} xyz=1 \\ x+ \dfrac{1}{z}= 5 \\ y+\dfrac{1}{x} = 29 \end{cases}$

Suppose that $x$, $y$ and $z$ are three positive numbers that satisfy the system of equations above. Then $z+ \dfrac{1}{y}= \dfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

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