In an equilateral \(\triangle ABC\), the side \(BC\) is trisected at \(D\) with \(BD= \frac{1}3 BC\). The value of \(\dfrac{AD^2}{AB^2}\) can be expressed as \(\dfrac{m}n \), where \(m\) and \(n\) are coprime positive integers. Find \(m+n\).

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