INDIRECT Reference to a Table to Sum data

Hello,

I have 12 individual tables all titled by a month in the year and includes data day to day. I am attempting to create a monthly roll-up table that sums up all this day to day info. I currently have it setup using a formula like this:

=SUM(January[Total '# of ATM Settlements])

What I'm hoping to gain some efficiency from is eliminating the need to update 'January' to each individual table's Month name. In my roll-up column A starting at A4 has each month's name. I'd like to try and make some sort of indirect reference using A4-A15 (January-December) to replace having to update this formula for each line. I found a formula out there and tried to update it as I thought I might work below, but it was by no means successful. Any help is much appreciated, if all else fails I'll just find and replace the month table name on all 12 lines but if I can avoid it, it'd be so much better.

=SUM(INDIRECT($A4&"[Total '# of ATM Settlements])"))