Michael's marbles

Two marbles are selected with replacement from a box containing \(R\) red marbles and \(B\) blue marbles. If the probability that one marble of each color is drawn is equal to \(\dfrac{15}{32}\), then the value of \(\dfrac{R}{B} + \dfrac{B}{R}\) can be expressed as \(\dfrac{a}{b},\) where \(a\) and \(b\) are positive coprime integers. What is the value of \(a+b?\)

This problem is posed by Michael T.

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