Tricky Equations

Algebra Level 4

\[\begin{equation}\begin{split}xyz=&3\\x+\dfrac1z=&4\\y+\dfrac1x=&5\\z+\dfrac1y=&\dfrac ab\end{split}\end{equation}\]

where \(a\) and \(b\) are coprime positive integers, find the value of \(a+b\).

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