On what threshold we should resample the data?
First of all, resampling or artificial sampling is not necessary nor panacea in many cases of imbalanced learning. Other methods may yield good results (eg threshold tuning, class weights adjustment and so on..).
That being said, resampling is indeed helpful in many cases of imbalanced learning.
But when do we have imbalance really? Is a 60-40 split imbalanced or not?
This is the heart of your question and cannot be answered fully (except for extreme cases) unless other methods are tried first and then resampling.
In many cases whether imbalance indeed is a problem depends on the case at hand and there are no hard limits (except of course extreme cases as mentioned above).
So first try other methods to adjust balance and then try resampling, is my advice.