To find the value of \( k \) in the equation
\[ 11 = -3k - 22 - 8k, \]
first, combine the terms on the right side of the equation:
\[ -3k - 8k = -11k. \]
This simplifies the equation to:
\[ 11 = -11k - 22. \]
Next, we can isolate \( k \) by first adding 22 to both sides:
\[ 11 + 22 = -11k, \] \[ 33 = -11k. \]
Now, divide both sides by -11 to solve for \( k \):
\[ k = \frac{33}{-11} = -3. \]
Thus, the value of \( k \) is
\[ \boxed{-3}. \]