In triangle \(ABC\), \(AB=\sqrt{30}\), \(AC=\sqrt{6}\), and \(BC=\sqrt{15}\). There is a point \(D\) for which \(\overline{AD}\) bisects \(\overline{BC}\), and \(\angle ADB\) is a right angle. The ratio \[\frac{\text{Area}(\triangle ADB)}{\text{Area}(\triangle ABC)}\] can be written in the form \(\frac{m}{n}\), where \(m\) and \(n\) are relatively prime positive integers. Find \(m+n\).

(第十四届AIME1996 第13题)