Fractions on a rectangle

Geometry Level 3

In the rectangle \(ABCD\) below, \(E\) lies on \(BC\) and \(F\) lies on \(CD\) such that the area of 3 triangles \(CEF\), \(ABE\), \(ADF\) are 3, 4 and 5, respectively.

If \(\dfrac {BE}{BC}+\dfrac{DF}{DC}= \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, what is \(a+b\)?

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