How did the Romans manage to effectively combine their whole empire into one unit?

The Roman empire was the greatest power in the Mediterranean in its respective time period, controlling trade through out the region and had the most powerful currency in the area. when Rome took over a territory, they allowed it to keep its religion and its own principles. Rome instead demanded a tax and in exchange the territory would become a part of the Roman empire. And as a part of the empire the territory would get to use the most widely accepted coin in the area. in modern relation it is what the dollar was about 2 years ago, the unquestioned currency that everyone in the area would take. it was of advantage to the territory to be part of the empire. Also if the incentives of membership and the right to keep their practices did not "do it" for the said territory, the legions of Rome that first took over it can always convince them to stay.