11. Billie has a die with the numbers $1,2,3,4,5$ and 6 on its six faces.
Niles has a die which has the numbers $4,4,4,5,5$ and 5 on its six faces.
When Billie and Niles roll their dice the one with the larger number wins. If the two numbers are equal it is a draw.
The probability that Niles wins, when written as a fraction in its lowest terms, is $\frac{p}{q}$. What is the value of $7 p+11 q$ ?