Piecewise-Defined Functions

Let

$$f(x) = \left\{ \begin{array}{cl} -x - 3 & \text{if } x \le 1, \\ \frac{x}{2} + 1 & \text{if } x > 1. \end{array} \right.$$

Find the sum of all values of $x$ such that $f(x) = 0$.