670 is certainly good enough for MBS. Your extra-curricular activities will certainly count in your favour - they are especially keen on people who have been active in the not for profit sector.
The major area of concern would be your work experience. You generally need to show some progression or initiative to get in if you only have three years experience so have a think on how you could sell yourself on this aspect. Having said this, there are many people in their mid twenties here so it certainly isn't impossible to make it after three years.
What country are you from? They tend to value a diverse class so if you are from a country that hasn't had many previous alumni you will have a better chance.
Good luck and check out my blog at http://www.mbamanchester.com