For a positive number $a$, on the closed interval $[ - a , a ]$, the function $$f ( x ) = \frac { x - 5 } { ( x - 5 ) ^ { 2 } + 36 }$$ has maximum value $M$ and minimum value $m$. Find the minimum value of $a$ such that $M + m = 0$. [4 points]
For a positive number $a$, on the closed interval $[ - a , a ]$, the function
$$f ( x ) = \frac { x - 5 } { ( x - 5 ) ^ { 2 } + 36 }$$
has maximum value $M$ and minimum value $m$. Find the minimum value of $a$ such that $M + m = 0$. [4 points]