I had this same problem with my Nexus 6P on AT&T. I was not getting LTE, only HSPA+. I figured my IMEI number was not added correctly to my account when I upgraded. So I called AT&T tech support, and first off let me give credit where credit is due, as I had my fair share of issues with AT&T. Talked to Jason, who was a super cool guy, not a robot, spent about 20 minutes troubleshooting my phone and my account settings. When the issue was resolved he even called me back to follow up. Could not be happier with the support I got.
Now onto the issue at hand. Turns out my IMEI number was correctly set on my account, and LTE was set as my Preferred network type under Cellular network settings. The issue was with my APN. The below change applies to both ATT Nextgenphone and ATT Phone APNs. Only this single line was changed from my original APN settings:
APN Type
default,admin,fota,mms,supl,hipri
The original setting did not include admin, and was in a different order. I was told the order actually matters. After this I am now getting LTE on both APNs and not HSPA+. I am using ATT Nextgenphone as I understand that with Marshmallow 6.0.1 VoLTE works on this APN.