Consider the function
$$f ( x ) = \begin{cases} - 3 x + a & ( x \leq 1 ) \\ \frac { x + b } { \sqrt { x + 3 } - 2 } & ( x > 1 ) \end{cases}$$
If $f ( x )$ is continuous on the entire set of real numbers, find the value of $a + b$. (Here, $a$ and $b$ are constants.) [4 points]