I have been having trouble with Visual Voicemail as well. I did not know it, but you must have cell data on to use it. If you have an iOS device, it is supposed to be covered by your data plan, but don't quote me on that because they frequently change their terms. It was $2.99/month if you are using another device. Again, they may've have changed their terms since I last looked. If you didn't sign up for it, ask a sales associate to assist you. If you do have it in your contract, try the following: I tend to lock my phone down so that I don't have unexpected charges, so only do this when you need to check your voicemail. Go to Settings-Cellular-Click The Switch next to it. The Switch will be green. Stay in this menu. Then make sure that only the apps that you want to access data are green by scrolling down. The app that you need for visual voicemail will be "Phone". Click the switch next to "Phone" and make certain that it is green. Assuming that you have visual voicemail set up properly, on your account, it should now work.
Sorry, answered the wrong one. I see that you have an HTC One. Try enabling cell data for your phone and see if it works for yours as well. I know that the iOS devices require cell data to use Visual Voicemail.
Thanks for the clarification about the fees. However, I replied twice, noting that OP was using and HTC One, once I saw it, so your response about OP using HTC One was unnecessary. Might I note that if you own an HTC One, that stating the steps to enable data so that they can use their visual voicemail may help the OP more than noting someone else's error.
Reporting times for posts lag and it could be that both posts were being created simultaneously where one is longer than the other but created before the other. Also note that the Inbox does not instantly update without a page refresh. Also note that OP has not returned in 5 months time.