\[\lim_{n \to \infty} {\dfrac{\left(1^{a}+2^{a}+3^{a}+ \cdots + n^{a}\right)}{{\left(n+1\right)}^{a-1} \left[\left(na+1\right) + \left(na+2\right) + \left(na+3\right) + \cdots + \left(na+n\right) \right]}} = \dfrac{1}{60}\]

Find \(a \in \mathbb{R^+}\) that satisfies the equation above.

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