i saw this one a forum but its for htc one m7 bit it worked for me
Phone: Verizon HTC One (HTC6500LVW)
Android version: 4.4.3
HTC Sense version: 6.0
Current SIM card and wireless provider: FYVE (online-only partner of Vodafone in Germany)
When I navigate to Settings > Wireless & Networks > Mobile Data (Network Settings) > GSM/UMTS Options > Access Point Names, I was originally just shown ONE access point. The three-dot menu option in the top right, which was allegedly supposed to allow me to add a new APN, contained only the option "Reset to default". Selecting this option would delete the only APN on the list with no option to add it back.
However, I found that navigating to Settings > Wireless & Networks > Mobile Data (Network Settings) > Preferred Network and switching from "GSM / UMTS" to "LTE / CDMA" and back again restores the single APN that you just removed.
Now, this single APN doesn't seem particularly useful. Selecting it brings up a whole bunch of fields (Name, Proxy, Port, Username, Password, Server, etc) that are all greyed out and uneditable. The only editable field is "APN", which I changed to "web.vodafone.de" (minus the quotes, of course -- this was given to me by my provider and should be available online for your provider as well).
However, this did NOT fix it.
What DID work, oddly enough, is switching BACK to LTE / CDMA mode and also changing the APN for this mode (in Settings > Wireless & Networks > Mobile Data (Network Settings) > LTE / CDMA Options > Access Point Names) to "web.vodafone.de". Then I switched BACK to GSM / UMTS mode...and it miraculously worked! I now have HSDPA connectivity.
I can't begin to explain why this worked. My hunch is that maybe the GSM / UMTS settings aren't writing anything to the APN field, but the LTE / CDMA settings are (since Verizon built the phone for its own LTE / CDMA network, it doesn't surprise me that this is the working part of their phone). But I am not a developer.
Maybe this will work for you, maybe not. It's obviously a poor implementation on either Verizon or HTC's part. Your mileage may vary. Good luck.