Too many variables!-2

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

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 $a+b.$