Configured the survey to be sent when we mark the ticket as closed, but it didn't work.

There are a few checks when a Satisfaction survey is not sent out. Check if this is an agent email address you are testing from. Check if the "When agent closes a ticket" notification under Admin--> Notifications--> Requester notification has been turned on. The same would be the case if you have set the survey to be sent out when a ticket is resolved. Turn on the "Agent Solves ticket" notification in the same page.