Unsure how to handle reporting a change of address to SSA

I receive SSI, and yesterday I moved to a different apartment. I paid this month's rent at my old apartment, and my mom paid this months rent and security deposit at my new apartment. I will start paying rent here every month next month. I know that I need to report the change of address to the SSA for my SSI. But I'm unsure how this would affect my benefits with me paying rent at the old place and my mom paying at the new place. I was getting the max amount ($967) at my old apartment. This apartment is more expensive than the old apartment because I don't have roommates.

Would they cut off my benefits for a month or two because of this situation or what would happen? Thanks!