Local Extrema Function Values

Consider a function defined by the equation:

$$ f(x) = 2x^3 - 3x^2 + ax + b $$

where $a$ and $b$ are constants. The function has a local maximum at $x = 1$ and a local minimum at $x = 2$. If $f(1) = 5$ and $f(2) = 3$, find the value of $a + b$.