Hola Garry

We sometimes omit elements when they are obvious so it doesn't sound redundant; this is why here you don't find -mente in the first adjective/adverb. It's understood by just using -mente in the last one that you mean internacionalmente y nacionalmente. 

As for the audio in that sentence "Me gusta este trabajo", I checked how it sounded and the narrator is simply extending a little bit that final -a in "gusta" - that is something very natural. It depends on each person but there is a tendency to do this as opposed to cutting off sounds at the end of each word as it would sound very robotic that way.

I hope this clarified it.

Saludos