2020 AIME I Problem 13

Point D lies on side \overline{BC} of \triangle ABC so that \overline{AD} bisects \angle BAC. The perpendicular bisector of \overline{AD} intersects the bisectors of \angle ABC and \angle ACB in points E and F, respectively. Given that AB=4,BC=5, and CA=6, the area of \triangle AEF can be written as \tfrac{m\sqrt{n}}p, where m and p are relatively prime positive integers, and n is a positive integer not divisible by the square of any prime. Find m+n+p.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.