(x4+y4)(xy+z2)3x3y4z3+(y4+z4)(yz+x2)3y3z4x3+(z4+x4)(zx+y2)3z3x4y3
Over all positive reals x,y and z, the maximum of the expression above can be expressed as nm, where m and n are coprime positive integers. Find m+n.
Source: VMO 2014 problem 2 day 2.