We can solve this equation by taking the square root of both sides: $x-6=\pm 5$.
Adding 6 to both sides, we get $x=6\pm 5$.
Therefore, the solutions are $x=11$ and $x=1$.
The sum of these solutions is $11+1=\boxed{12}$.
The answer is: 12
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Find the sum of all solutions to the equation $(x-6)^2=25$.

### Answer:
