Olympiad Corner 2

Algebra Level 4

For positive reals \(x\) and \(y\) satisfying \(3x + 4y = 5\). If the maximum value of \(x^{2}y^{3}\) can be expressed as \( \dfrac AB\) for coprime positive integers \(A\) and \(B\), find the value of \(A+B\).

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