Angle \( \alpha \) is in quadrant III and angle \( \beta \) is in quadrant IV. If \( \sin \alpha = - \frac { 5 } { 6 } \) and \( \cos \beta = \frac { 1 } { 2 } \) , find \( \cos ( \alpha + \beta ) \) .
\( \frac { \sqrt { 11 } + 5 \sqrt { 3 } } { 6 } \)
\( \frac { \sqrt { 11 } 5 \sqrt { 3 } } { 6 } \)
\( \frac { \sqrt { 11 } 5 \sqrt { 3 } } { 12 } \)
\( \frac { \sqrt { 11 } | 5 \sqrt { 3 } } { 12 } \)