Triangle trials

Geometry Level 3

\(ABC\) is a triangle with centroid \(G\) and side lengths \(AB=15, BC=18,AC=25\). \(D\) is the midpoint of \(BC\). The length of \(GD\) can be expressed as \( \frac{ a \sqrt{d} } { b} \), where \(a\) and \(b\) are coprime positive integers and \(d\) is a square-free positive integer.

Find \( a + b + d + 1 \).

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