CE-680 Captain reported an engine failure during cruise. The engine was shut down and the aircraft landed safely.

Narrative

On Day 0 at approximately XA:55 hours I had just leveled the aircraft at FL250 per ATC request. I heard a loud bang and vibrations coming from the right engine of the CE680. I confirmed with my copilot and the engine instruments that we had a right engine failure. My copilot [requested priority handling] and stated that we had an engine failure to ATC. ATC failed to acknowledge my copilots request. My copilot [requested priority handling] a second time and the ATC continued to give other aircraft instructions. It was not until an airline pilot instructed ATC to answer our call that our [priority handling] was acknowledged. During this time I confirmed the right engine had failed and the ITT (Interstage Turbine Temperature) was still climbing. I had the copilot confirm this information. I brought the right throttle to idle. The ITT continued to climb. I shutdown the right engine by moving the right throttle to the fuel cutoff detent. The ITT decreased on the right engine. At this time my copilot was able to communicate with ATC and a decent and heading to the south was given for a planned runway X arrival at ZZZ. The engine shutdown checklist was completed and the single engine approach checklist was completed. The decent; arrival and landing were uneventful on a single engine. We requested the firetrucks be available on arrival. I briefly stopped on the runway in front of the fire trucks to confirm that there was not a fire. After no fire was confirmed I taxied to the FBO followed by the firetrucks. After shutdown on the ramp I met with the fire fighters who inspected the aircraft and determined no reportable damage was observed. I met with an official who took a picture of my pilot license and took my contact information for his report. As of this report an engine inspection by the manufacture is planned but not started.