\[\begin{cases} x+y=5xy \\ y+z=6yz \\z+x=7zx \end{cases}\]

If \(x,y\) and \(z\) satify the above system of equations, then the value of \(x+y+z\) can be expressed as \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. Submit your answer as the value of \(a+b.\)

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