Largest Cubic Sum

Algebra Level 4

Find the largest possible value of x3+y3+z3x^3+y^3+z^3 for real x, y, z,x,\ y,\ z, such that {xyz2=64y128xx2yz=32y32z3xy2z=128x64z \begin{cases} xyz^2=-64y-128x\\ x^2yz=-32y-32z\\ 3xy^2z=128x-64z \end{cases}

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