figuratuvely used in the sense of nutrient source used to feed microorganisms. See:

My point is, "culture broth" is far more common than "broth of culture", in spite of the fact that most references to the first are in the field of biology.

http://www.geocities.com/RainForest/1820/economy.htm
Rich in cultural manifestations provoked by its several etnias, the tradition pantaneira forms an alliance with a marvelous contemporary artistic production, creating a vigorous *culture broth*, capable to seduce and to conquer visitors of the most several origins.

http://www.scienceblog.com/community/older/archives/L/2001/A...
The drug problem and organized crime in general undermine institutional frameworks, conspire against democracy, cause governance to deteriorate and plant death and violence. They are a *culture broth* for corruption, eroding judicial systems and hindering the rule of law.

http://arts.zambezitimes.com/fullarts.php?idarts=69
People from all over the world know the great musical *culture broth* that is waiting (So as the African football was) "hidden in the gloom" around the African corner, which calls aloud for ACTION towards its boiling point.

For the explanation you've provided, I think "culture broth" or "cultural broth" does not make sense as an answer because if you google it, you'll find that there is actually something involving microbiology and things like that, which does not convey the meaning you seek for. When I was looking for it, I found it on WordReference, and then googled it as a form of corpus search, and found that "melting pot" is better for this kind of thing. Other suggestions: "kaleidoscope", "multiculturalism", "salad bowl", "[cultural] mix".