I am half-Russian, half-German speaker of English and I am working hard to reduce my accent. I fully agree with one of the reviewers who said that the book is disappointing in the sense that it is basically your regular beginner's pronunciation course, like Sheep or Ship, Three or Tree, served under a different title (to boost sales???).
It does NOT offer any advice on how words are linked in speech and how it affects their pronunciation, neither does it say anything on intonation, sentence stress depending on the type of sentence etc., i.e. information that is vital for advanced speakers.
There are proper accent training books for actors, such as the one published by Penny Dyer who provides speech training for actors and actresses. You can tell immediately that those are the books designed for professional actors as a larger portion of the material is dedicated to longer speeches that allow one to practice complex intonation, varying pace, enunciation and sentence stress.
Also, I found English Pronunciation in Use Advanced by Martin Hewings A LOT more helpful and thorough. After all, most intermediate and advanced speakers might be able to pronounce individual words well enough, but it is often tempo, intonation and word linkages in flowing speech that may give them away as non-native speakers.