Galaxy Note 3 ATT SM N900A - rooting failed and the unlock bootloader question

I have an ATT Note 3 that was on 5.1, but I downgraded to 4.4.4 to see if I could get it to root. I have tried all of the available rooting options (towelroot, KingRoot, KingoRoot, iRoot etc) none of them work. Towelroot gives me the standard modstring error that I tried fixing with available codes, but that didnt work wither. So , my question is how do I work around the fact that I cannot get my phone to root and then do I need to unlock the bootloader or should I be able to install Safestrap after I get it rooted so I can load my ROMs? What other options are there for rooting the phone at this point?

Any help please!

thanks muchly

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