Simple System of Equations Part 2

xy+z=26xz+y=29yz+x=34 \begin{aligned} xy+z&=&26 \\ xz+y&=& 29 \\ yz+x&=&34 \end{aligned}

If x,y,zx,y,z are integers satisfying the system of equations above, what is the value of x+y+zx+y+z?

See Part 1 and Part 3.

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