To find the sum of \(\frac{3}{4}\) and \(-\frac{11}{4}\), we can simply add the two fractions since they have a common denominator:
\[ \frac{3}{4} + \left(-\frac{11}{4}\right) = \frac{3 - 11}{4} = \frac{-8}{4} \]
Now, we can simplify \(\frac{-8}{4}\):
\[ \frac{-8}{4} = -2 \]
Thus, the sum of \(\frac{3}{4}\) and \(-\frac{11}{4}\) is \(-2\). This answer is already in its lowest terms.
The final answer is:
\[ \boxed{-2} \]