If this ever happens again, do what you can to mitigate the damages.
Call a plumber, let your landlord know.
Yes, you could be required to pay, but that payment could eventually be used to offset future rent.
You might even be able to sue the landlord and recover the money.
Get yourself a renters insurance policy that covers these water awards and damages, discuss it with your agent.
Renters policy are very cheap, compared to what you'll be dealing with in the coming weeks.
Also meet with the landlord or his agent and ask how this should be handled if it ever reoccurs.
Ask for some written instructions, be cooperative, and be ready to discuss emergencies in general even if you move.
Plan for life, don't just be reactive, be proactive and engaged.
Let us know what happens.