Dragon respawns faster than 6 minutes.
In a recent game a friend was playing, the enemy team had 3 dragons at 18 minutes and 53 seconds. Dragon is supposed to spawn at 2:30 and then respawn every 6 minutes after that. So the earliest this should happen is at 20 minutes and 30 seconds if you kill dragon the moment it spawns. Unfortunately I only have a LOL Replay file for this game.