Length of AC makes me cry?

Let $I$ be the incenter of a triangle $ABC$ and let $AI,BI$ and $CI$ intersect $BC,CA$ and AB at $D,E$ and F respectively. If $AB=20$ , $BC=14$ and $AC=\frac{438}{53}$ , then $\frac{ID}{IF}$ = $\frac{a}{b}$ for positive coprime integers $a$ and $b$ . Find the value of $a+b$ .