Hi there...did you ever have an old injury at that part of your back?
On the Master-Cleanse people will find that they get strange aches and pains - because you're not using energy up on digesting food the energy in your body can go where it is needed. Perhaps some healing is taking place at this spot in your back?
I wouldn't worry about 5 or 10 days on the MC...unless you get dizzy and start to feel reeeeally bad, this kind of pain is okay. If you can get someone to rub the area that's a good idea...it brings more energy to the area...sounds like some stagnant qi.
I don't know why your pain would go away eating cheeseburgers! hmmm. You're thinking it has something to do with protein? Being deficient in B12 or something? hmmmmm You can always get that tested.
Because you say it subsides when you stop drinking liquids maybe this pain has something to do with your kidneys? In which case you're doing exactly the right thing.... The Master Cleanse totally cleans your kidneys....so keep it up and don't worry....if (and it's a long-shot) you're not getting enough nutrients, it's only for a few days...but listen to your body, like I said before, if you feel sick sick or dizzy then you might want to quit.
You should do a search on curezone's search engine for this kind of back pain and link it with kidneys....do some searching and you might find some answers!