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A quadrilateral is said to be bicentric if there exists a circle that is internally tangent to each of its sides, and another circle that contains all of its vertices. Let $ABCD$ be a bicentric quadrilateral with $AB = 25$, $BC = 37$, and $CD = 49$. If $O$ and $I$ are the circumcenter and incenter of $ABCD$, respectively, the distance $OI = \dfrac{m}{n}$ for some coprime positive integers $m, n$. Find $m + n$.