Olympiad Geometry · Hard problem

In $\triangle ABC$, point $D$ is on $\overline{AB}$ and point $E$ is on $\overline{AC}$. We know $m\angle ADE = (3x + 5)^\circ$, $m\angle ABC = (4x - 10)^\circ$, and $m\angle AED = 58^\circ$. If $\overline{DE} \parallel \overline{BC}$, find $m\angle A$.