For the curve $y = x ^ { 3 } - a x + b$, the slope of the line perpendicular to the tangent line at the point $( 1,1 )$ is $- \frac { 1 } { 2 }$. For the two constants $a$ and $b$, find the value of $a + b$. [4 points]
For the curve $y = x ^ { 3 } - a x + b$, the slope of the line perpendicular to the tangent line at the point $( 1,1 )$ is $- \frac { 1 } { 2 }$. For the two constants $a$ and $b$, find the value of $a + b$. [4 points]