When a Rectangle and Cube are Summed!

Algebra Level 3

Let \(f(n) = \dfrac{g(n)}{h(n)} \), where \(g(n) = 1^3 + 2^3 + \cdots + n^3\) and \(h(n) = 2 + 6 + 12 + 20 + 30 + \cdots + n(n+1)\).

If the value of \(f(100) \) can be expressed as \( \dfrac mn\), where \( m\) and \(n\) are coprime positive integers, find \(m+n\).


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