I recently upgraded my OnePlus One to Android 6.0.1 and while I can make phone calls I don’t have any network connectivity unless I’m on WiFi. The symptoms are;

• Can’t send email,
• No access any websites
• Phone is not on a LTE network

This awkward fix, posted byrohitvermamech on the OnePlus Forums  get’s LTE and networking working again:

Step 1:
Go into Settings > Mobile Networks > Access Point Names > Restore Defaults
The list should now have many many more choices of APNs. Choose the correct APN. Then go into Settings > Mobile Networks > Network Operators (make sure you are connected to WiFi) click “Choose Automatically”. Then turn Aeroplane Mode on and back off.
Step 2:
VERY IMPORTANT! Restart your phone.
Step 3:
Go into phone and dial *#*#4636#*#* and choose Phone Information. In Phone Information set the Preferred Network Type to LTE/GSM auto (PRL) [even if it says it already, do it again]. Turn off the radio. When the radio is turned off, turn the radio back on. Go down to the SMSC and hit “Refresh” and then “Update”.