To evaluate the given expression, we need to follow these steps:
First, we calculate the value inside the absolute value function: \[ 11 - 15 = -4 \]
Next, we apply the absolute value to the result: \[ |-4| = 4 \]
Finally, we negate the result from the previous step: \[ -4 \]
\[ \boxed{-4} \]
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