The best, and probably the only way to improve your English dramatically in just one month is immersion. If you are able to place yourself in a situation where you have to to live your life entirely in English, one month can make a big difference, especially if you are young. Regrettably, however, it tends to be very costly to arrange such a situation. Two months are better than one.
In composing this reply I am relying on my personal experience of becoming fluent in French. My mother was a native speaker of French and I studied French at school, but not until I had six weeks of immersion was I able to become fluent.