The cosine summation

Geometry Level 4

The value of $\displaystyle\sum_{r=0}^{12} \binom{12}{r} \cos \frac {r\pi}{6}$

is of the form $-(x+\sqrt {y})^{z}$ , where $x,y$ and $z$ are integers, and $z$ is as large as possible.

Find $x+y+z$ .