My understanding is that they don't remove a significant amount of nutrients. Algae grows faster and removes more. Julian Sprung recommends 1 small mangrove per 1-2 gallons of water if you want to try a mangrove "filter": https://www.twolittlefishies.com/images/mangrove_manual.pdf
I don't think a mangrove is any better than a few corals or some macroalgae. The best way would be to feed less if nutrients are your concern. Get mangroves because they're cool otherwise you probably won't keep it alive long.