B787 Captain reported a left air conditioning pack failure resulted in an air turn back and fuel dump to get below max landing weight.

Narrative

I was the Captain on flight from ZZZ1 to ZZZ2. We were dispatched with a deferred pressurization CAC-L1 due to a left air conditioning pack and CAC-L1 failure on the inbound flight. Preflight; taxi; take-off; climb all normal. Shortly after reaching cruise at FL350 we heard the left pack shutdown and received an Engine Indicating and Crew Alerting System message of 'Pack L indicating the left pack failed. We completed the appropriate checklist and the pack remained 'failed'. We are now in single pack/pressurization with a XA:05 flight over the North Atlantic; Europe to ZZZ2. We called for the two relief pilots to return to the flight deck to assist in the divert and additional work load. We contacted with Company Dispatcher and maintenance via our SAT phone to discuss the issue and determine best course of action. Continuing to ZZZ2 was ruled out and diversion back to ZZZ1 was decided as the best course of action. Fuel dump would be required to get down to max landing weight. We coordinated with cabin crew for the divert. Advised passengers of the situation and that a return to ZZZ1 was required and was the safest course of action due to the mechanical situation we were having. Obtained clearance from ATC for return to ZZZ1 and clearance for fuel dump. Approximately 20 minutes of dump was completed (approximately 80K lbs. of fuel) and logged. Descent; approach into ZZZ1 were normal until we received an Engine Indicating and Crew Alerting System 'Pack Altitude Limit' message indicating insufficient equipment cooling airflow and the equipment cooling is now in the override mode. Normal landing in strong; gusty crosswinds. Taxi to gate normal. After aircraft parking; shutdown and checklists I called to debrief dispatcher; (maintenance controller); FODM (flight operations duty manager). Debriefed ZZZ1 local maintenance on the plane. The entire cockpit crew was very helpful and professional in helping coordinate the divert; fuel dump; etc. during this flight. The extra pilots added a very useful backup during this event to safely return to ZZZ1. Please contact me with any questions or concerns regarding this flight."