I've only flown into FCO once--on a Schengen flight and with carry-ons only. I made a rookie mistake by waiting in a huge line at the Trenitalia kiosk at baggage claim instead of walking directly to the Leonardo Express (where there were plenty of kiosks and no lines). Since you will already have the Leonardo Express tickets, it would simply be a matter of how long it will take to go through passport control, collect your bags, and walk to the train platform. As someone noted above, it took just over an hour. Plus add 32 minutes for the Leonardo Express, and then time trying to navigate Termini for your next train.

I'll leave it to the experts on how much time you should allow. I'm not sure if you actually meant 10:35am or 11:35am. If the latter, I would go for that and then you won't have to stress unless your flight is very delayed.