You shouldn't have tooo much trouble. Just get yourself a 52 inch cue for the ends of the table. They aren't much different to cue with then a full length cue. You only got about 4 feet 4 inches on each end of the table, but slightly more room if you only include the playing area. Your actual play area is only 38" x 76" or 3 feet 2 inches x 6 feet 4 inches, leaving you 4 feet 8 inches at each end or 56 inches. For a full length cue in with a table that size you need these dimentions. 12' 11" x 16' 2" Your only 2 inches short at either end of the table.
In conclusion, YES you should have plenty of room. I would put that size table in that size room.
