B767 Captain reported a rising cabin altitude due to a Main Cargo Door malfunction; resulting in an emergency descent and landing at a diversion airport.

Narrative

Main Cargo Door EICAS message and Cargo doors light illuminated at cruise FL350 time XA51. We also had rising cabin altitude. No other indications prior to the EICAS message. I did feel light headedness and the onset of possible hypoxia symptoms as the cabin altitude rose prior to descent. I was the PF and FO was the PM. FO initially ran the QRH. We then swapped controls and I completed the QRH and managed communications while the FO descended us to 10;000 feet per the QRH. We [requested priority handling] with ZZZ Center. We communicated with Dispatch via ACARS with the nature of the event and our dispatcher was extremely helpful throughout the event and divert process. After leveling at 10;000 feet; EICAS message and Cargo Doors light extinguished after approximately 2 minutes. ZZZ was 40 miles to our north at that point and we concluded that it was dour best divert option. ZZZ approach gave us delay vectors on an extended downwind for runway XXR as we finished our checklists and briefings. I took the airplane back as the PF at approximately 16 NM from the airport and we were cleared for the visual approach ZZZ runway XXR. Uneventful approach and landing. Crash fire rescue was right there waiting for use when we exited the runway. Maintenance in ZZZ was very professional and was ready to troubleshoot as soon as we got there. The ground personnel trans-loaded the freight to another airplane and we then completed our pair flying ZZZ-ZZZ1 without incident.Cause: Possible mechanical issue with the main cargo door.