I've created a dummy objective, 'time' and have a 1 second repeater clock adding 1 to the score for @a every second. I then have a command block that will execute a /testfor to check when the score '600' is met and a comparator will light up a redstone lamp to say when 10mins has passed. What command would the /testfor command block need?
This command should be what you want:
This will only give a weak output, so make sure to have a repeater after the comparator.