To find the sum of \( p \) and \( q \), we have:
\[ p = \frac{3}{4} \] \[ q = -\frac{11}{4} \]
Now, we can calculate \( p + q \):
\[ p + q = \frac{3}{4} + \left(-\frac{11}{4}\right) \]
Since both fractions have the same denominator, we can combine them directly:
\[ p + q = \frac{3 - 11}{4} = \frac{-8}{4} \]
Reducing the fraction:
\[ \frac{-8}{4} = -2 \]
Thus, the sum of \( p \) and \( q \) is:
\[ \boxed{-2} \]