I do not believe that anything can ever bring an end to drudgery. Technology has certainly reduced the demand for some jobs that could be classified as drudgery, but it has given rise to other such jobs. In addition, there are some jobs that will never be able to be done by technology.
Let us look at some jobs in which humans can never be replaced by technology. A perfect example is housekeeping jobs in hotels. It is highly unlikely that robots will be created that can clean and make up hotel rooms every day as effectively and cheaply as humans can. This is a job that is (to me, at least) drudge work and which cannot be done by machines.
In addition, there are some jobs that can be seen as drudge work that are actually caused by technology. For example, hooking up cable TV is a job that was created by technological advances. I would argue that that job involves drudge work.
There will always be many jobs that will be uninteresting and repetitive and will have to be done by human beings.