Minimum Value

Algebra Level 4

If \(x\) and \(y\) are real numbers such that \(5x+12y = 60\) and the minimum value of \( \sqrt{x^2+y^2} \) is equal to \( \dfrac ab\) for coprime positive integers \(a\) and \(b\), find the value of \(a+b\).

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