To find the slope of the line given by the equation \( y - 11 = -12(x + 1) \), we can rearrange the equation into slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope.
Starting with the equation:
\[ y - 11 = -12(x + 1) \]
First, we distribute \(-12\) on the right side:
\[ y - 11 = -12x - 12 \]
Next, we add \(11\) to both sides to isolate \(y\):
\[ y = -12x - 12 + 11 \]
Simplifying the right side gives:
\[ y = -12x - 1 \]
From this equation, we can see that the slope \(m\) is \(-12\).
Thus, the slope of the line is \(\boxed{-12}\).