I personally don't like the word "detox". To me it makes me think of faddy diets (rightly bit wrongly).
I highly recommend the 8 week sugar diet by Dr Michael Mosley. It gives you the science behind his diet, whether or not you follow his diet.
I have never had a sweet tooth but after I followed LCHF for a few weeks, I tried to eat one of my favourite raspberry ice lollies. It was disgusting! I was cured!
I relapsed a few times on LCHF, the carbs were calling to me and I binged on crumpets or ryvitas. I stuck with it, I no longer have cravings.
I find you are concerned about sugar, LCHF is not so much a quick short term diet, more a way of life.