Consider a circle \(C\) with center \(O \) and radius \(R=3\). \(ABC\) is a triangle inscribed in \(C\) such that \(BC = 5\) and \(\angle ABC = 60^\circ \).

Given that the area of the triangle \(ABC\) is equal to \( \dfrac{a\sqrt b(a + \sqrt c)}d \), where \(a,b,c\) and \(d\) are positive integers with \(b,c\) square-free and \(d\) minimized. Find \(a+b+c+d\).

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