JetBlue 35/40 min connection

Hi! JetBlue Vacations booked flights from Buffalo to FLL then FLL to Cancun. I just checked and my flight lands in FLL at 10:20am in terminal 3. Then departing flight from FLL to Cancun leaves at 11am with doors closing at 10:45am in TERMINAL 4. I am stressed and JetBlue assured me it’s enough time. Do I need to go through security again in terminal 4? Anyone ever made this tight of a window?