coccassi function algebra

Algebra Level 3

\[ x + y = 5 xy \\ y + z = 6yz \\ z + x = 7 z x \]

If \( xyz \neq 0 \), then the value of \( x+y+z \) can be expressed as \( \frac{a}{b} \), where \(a\) and \(b\) are positive coprime integers. What is \(a+b\)?

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