Solving D S.'s system of equation

Algebra Level 5

For all pairs of nonzero real numbers \((x,y)\) such that \(24x^3 − 10x^2y − 3xy^2 + y^3 = 0\) and \(x^2 + 5x = y^2\), let \((a,b)\) denote the solution with the largest value of \(x\). What is the value of \(a + b\)?

This problem is posed by D S.

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