Consider the function $S ( a )$ defined by the limit below:
$$S ( a ) : = \lim _ { n \rightarrow \infty } \frac { 1 ^ { a } + 2 ^ { a } + 3 ^ { a } + \cdots + n ^ { a } } { ( n + 1 ) ^ { a - 1 } [ ( n a + 1 ) + ( n a + 2 ) + \cdots + ( n a + n ) ] }$$
Find the sum of all values $a$ such that $S ( a ) = \frac { 1 } { 60 }$.