well, no, it is not good to detox until you get the mercury out. it will just put more in your brain and you can get sick. there are some products out there that say they do not disturb mercury and you can detox with them if you still have fillings. i am not a scientist and don't know for certain if it is true, but i would not do it.
the last mercury filling i got, i asked for white. he put in mercury and then said later, it didn't lend itself to a white one. half my body went numb and stayed that way for days. it was difficult to walk. it was at that point i said i will never get another mercury filling.
there must be some dentist out there who is mercury free who has a heart and will let you make payments on a filling. call around. it isn't good to drill it out, but it's worse if they put a mercury one back in.
i don't believe in liver flushes anyway, so you are talking to the wrong person, but no, with mercury in your teeth, i would not do any flushing or fasting or anything.