You'd know if it was your gums, they'd be bright red and shiny, not pink. They also wouldn't bleed that profusely if you're accurate in how much you bled.
However if you had a cut you would expect it to carry on bleeding after brushing, whereas gums tend to stop pretty quickly.
Given that you can't find a source and it was a lot of blood I would reccomend you see your doctor or dentist.
To be on the safe side when you brush next, brush gently and in little circles. Use a soft-bristled brush if you have one.
If you want to try and rule out a nosebleed have a check up your nose and try to see if there is any caked in blood on the walls of the nostril.