ANSWER: Use “cannot”.
Sometimes “can not” causes a noticeable stress problem in English. If we write “I can not believe it”, we are adding the possibility of an unintended extra emphasis on “not”. It could be that this stress is too much for the meaning you wish. It is almost like stamping your feet on the word “not”!
In preference, “cannot” will always work well in English, with no undue or unintended stress – unless, of course, you wanted to stamp your feet! But in IELTS writing, candidates all too often write that they strongly believe in something when it is clear the arguments they have made are not very strong at all. This artificial emphatic belief can make the candidate appear too dramatic. Formal essays are best written objectively and dispassionately.
Contractions such as “don’t” and “can’t” should never be used in an IELTS essay (or any other formal essay?). But the exception is sometimes when you are writing a letter in Task 1 for the General Training Module. Contractions can be OK, if, for example, the letter is written to a friend and is therefore less formal. If you are writing a letter to a business etc., we suggest you play it safe and use “cannot” or do not”.