What is the sum of all values of y for which the expression \(\frac{y+6}{y^2-5y+4}\) is undefined?
If we simplify that expression we get: \(\frac{y+6}{(y-1)(y-4)}\). The expression is undefined when the denominator is equal to 0 which is when y=1 or 4. So the sum of 1 and 4 is \(\boxed{5}\).