To find the sum of \( p \) and \( q \):
\[ p = \frac{3}{4} \] \[ q = -\frac{11}{4} \]
Now, we add \( p \) and \( q \):
\[ p + q = \frac{3}{4} + \left(-\frac{11}{4}\right) \]
This can be simplified as:
\[ p + q = \frac{3}{4} - \frac{11}{4} = \frac{3 - 11}{4} = \frac{-8}{4} \]
Now, we simplify \( \frac{-8}{4} \):
\[ \frac{-8}{4} = -2 \]
Thus, the sum of \( p \) and \( q \) is:
\[ -2 \]
The answer is \( -2 \), and it is already in lowest terms. Therefore, the final answer is:
\[ \boxed{-2} \]