Android 5.1.1 sent OTA to AT&T's Samsung Galaxy S6 and Samsung Galaxy S6 edge7
Because the update is being sent out on a staggered basis, you might not see it hit your phone for a few days yet. Don't let your feelings get hurt, eventually you will receive a notification that the update has arrived. If you are impatient, you can try to manually shake out the notification by going to Settings > About device > Software update.
Once you are ready to begin the updating process, make sure that you are on a Wi-Fi network in order to save your precious data. And your battery should be charged to at least 50%. Having your phone shut off because the battery died while in the middle of performing an update, can sometimes lead to problems with your handset.