Bottom bracket replacement advice needed for BBright BB386EVO
This frame either uses a BB386 Evo "standard" or a Pressfit 30 "standard". You can determine which by measuring the width of the frame at the BB shell. If 86.5mm it is BB386Evo. If 68mm it is Pressfit 30. 

If it is a Pressfit 30(68mm shell) this BB is a direct fit for the Shimano crank without extra spacers. this is the PF30 version of the BB30 bottom bracket that @bikebum listed in his answer. 

However, based on the markings on your existing crank, I believe it is BB386 Evo.   


  To add to the confusion, the crank actually says 'For BBright BB386EVO'


That means that it is a pressfit(non-threaded)frame, with a shell width of 86.5mm, and an outside bearing race(cup)diameter of 46mm. The inside diameter of that bearing cup is 30mm. 

MegaExo is a brand of bottom bracket made by FSA, not a measurement standard. 

Any Pressfit 30 BB kit, like the ones from SRAM or Wheels Manufacturing will fit the frame. Nothing else will fit. 

To fit a crankset, you either need a BB386 Evo crank, as you have now (also known as the "long BB30"), or you need a spacer kit to adjust he diameter of your frame's required standard of 30mm to the crank you want to use. 

Since the Shimano crankset is designed for an 86.5mm frame, you only need to adjust the ID of the bearing cup to 24mm Shimano standard. 

A Wheels Manufacturing 24mm to BB386 Evo adaptor like this one does the trick. 

FSA makes a good BB reference poster here.