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Given that xyz=1xyz=1xyz=1 where x,y,zx,y,zx,y,z are positive real numbers and that x+1z=5x+\dfrac{1}{z}=5x+z1=5, y+1x=29y+\dfrac{1}{x}=29y+x1=29 and z+1y=mnz+\dfrac{1}{y}=\dfrac{m}{n}z+y1=nm, where mmm and nnn are coprime positive integers. Compute m+nm+nm+n.
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