Two of the roots of the equation \[ax^3 + bx^2 + cx + d = 0\] are \(2 - \sqrt{3}\) and \(5\), where \(a,b,c,d\) are rational numbers.
If the third one is \(m + \sqrt{n}\) for some integers \(m\) and \(n\), find \(m + n\)

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