The daytime fixed rate cab fare from FCO is 40 Euro or a little over $60. If you do ride the train to Termini and then take a cab, you will be paying the 11 Euro x 2, plus the cab fare from Termini (? - 10 to 15 Euro). You are starting to get pretty close to that 40 E total for the full ride.
If you do opt to take the train into town and want to continue on using public transportation, "From the Roma Termini train station take underground line A towards Battistini and get off at Flaminio."
Romelle