Largest Cubic Sum

Algebra Level 5

Find the largest possible value of \(x^3+y^3+z^3\) for real \(x,\ y,\ z,\) such that \[ \begin{cases} xyz^2=-64y-128x\\ x^2yz=-32y-32z\\ 3xy^2z=128x-64z \end{cases} \]

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