Finally I discovered a solution. Someone else in my household uses the same model phone but theirs is on stock TouchWiz. Using APN Backup and Restore I backed that phone's APNs.
Now for what I did after backing up the working APNs and for you need to do to fix your phone. You're ROM must support root access. While I'm not quite sure I believe you also need a custom recovery. (You probably have one already since you flashed your custom ROM) So I would recommend using CWM or TWRP. This may be necessary to convert a user app into system app.
Once you have this download the file I've attached. Do not rename it since the app you will be using requires it to be named that way. Go to the Play store and download HiAPN. You will need to give it root access and make it a system app. It will prompt you to do so. The reason it needs all these permissions is to access the APNs. Once you've done this use the restore feature and select the file. The file you downloaded must be in the folder for HiAPN. ~/HiDroid_Net/HiAPN Once this completes, check that the Network Mode in your settings is set to LTE/CDMA/EvDo. HiAPN may change it to a GSM mode which is incorrect. Then just go ahead and restart your phone. The final step is demote HiAPN and remove it if you choose to. It's requesting many permissions and it's partially in a foreign language. (What you need to do is in English) You can use an app like Titanium Backup to remove it since you can't the normal way because it's currently a system app.
I truly hoped this helped you since it helped me. Feel free to ask questions and I will answer them to the best of my knowledge.
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