For any two points M and N in the X Y -plane, let M N denote the...

For any two points $M$ and $N$ in the $X Y$-plane, let $\overrightarrow{M N}$ denote the vector from $M$ to $N$, and $\overrightarrow{0}$ denote the zero vector. Let $P, Q$ and $R$ be three distinct points in the $X Y$-plane. Let $S$ be a point inside the triangle $\triangle P Q R$ such that $\overrightarrow{S P}+5 \overrightarrow{S Q}+6 \overrightarrow{S R}=\overrightarrow{0}$. Let $E$ and $F$ be the mid-points of the sides $P R$ and $Q R$, respectively. Then the value of $\frac{\text{ length of the line segment } E F}{\text{ length of the line segment } E S}$ is ________