Value of Determinant

Algebra Level 3

\[ \begin{vmatrix}{1/1} && {1/3} && {1/15} \\ {1/3} && {1/15} && {1/35} \\ {1/5} && {1/35} && {1/63}\end{vmatrix} \]

If the value of the determinant above equals \( \dfrac AB\), where \(A\) and \(B\) are coprime positive integers, find \(A+B\).

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