1991 AMC 12 Question 19

Triangle $ABC$ has a right angle at $C,$ $AC=3,$ and $BC=4.$ Triangle $ABD$ has a right angle at $A$ and $AD=12.$ Points $C$ and $D$ are on opposite sides of $AB.$ The line through $D$ parallel to $AC$ meets $CB$ extended at $E.$ If $$
\frac{DE}{DB}=\frac mn,
$$ where $m$ and $n$ are relatively prime positive integers, then $m+n=$