I did a quick search for info about living at high altitude. One article I read said that roughly 22,000 feet is the limit for humans to live long term without supplemental oxygen. The article cited a study where a number of people lived at 22,000 feet without supplemental O2 for a period of two years.
So, I guesstimate that an average person can live for 10 minutes at 35,000+ feet. I couldn't find any info on how long a person can be expected to live at that high an altitude.