Paper Folding Rectangle Perimeter

$ ABCD $ is a rectangular sheet of paper that has been folded so that corner $ B $ is matched with point $ B' $ on edge $ AD. $ The crease is $ EF, $ where $ E $ is on $ AB $ and $ F $ is on $ CD. $ The dimensions $ AE=8, BE=17, $ and $ CF=3 $ are given. The perimeter of rectangle $ ABCD $ is $ m/n, $ where $ m $ and $ n $ are relatively prime positive integers. Find $ m+n. $ [Asymptote diagram]