Academically, the most valuable experience for me was a massive improvement in the most basic skills that any lawyer must possess, that is, critical thinking, analytical thinking, and writing skills.
Do a masters if you believe it will truly add value to you. If along the way you do get a job abroad, give yourself a pat on the back and grab it!
A lot of people ask me, Why did you “switch” from Law to Media and I always say, "It is never a switch. I cannot stop being a lawyer."
The reasons for you to do the LL.M will always be unique to you, so you must always look at this bigger picture, and use external advice (including this interview) only to fill informational voids.
In case you are thinking about an LLM from the London School of Economics and Political Science (LSE), here is a good opportunity to find out more.