Olympiad Geometry · Hard problem

In $\triangle ABC$, point $D$ is on $\overline{AB}$ and point $E$ is on $\overline{AC}$ with $\overline{DE} \parallel \overline{BC}$. The lengths are $AD = x$, $DB = 4$, $AE = 6$ and $EC = x - 5$. Find $AB$.