The expression $\frac{y+6}{y^2-5y+4}$ is not defined when the denominator is equal to 0.
We can factor the denominator as $(y-4)(y-1)$, so the expression is not defined when $y=4$ or $y=1$.
The sum of these values is $4+1=\boxed{5}$.
The answer is: 5
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Find the sum of all values of $y$ for which the expression $\frac{y+6}{y^2-5y+4}$ is not defined.

### Answer:
