The top of a broken tree has its top end touching the ground at a distance of \(15m\) from the bottom. The angle made by the broken end with the ground is \(30^{\circ}\). Then find the length of the broken part.

Express your answer in the form of \(a\sqrt{b}m\), where \(a\) and \(b\) are coprime positive integers. Enter the value of \(a+b\).

This problem is part of the set Trigonometry.

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