Translation:I am bilingual, but I cannot speak English.
These comments really helped. I managed to get it right, but I couldn't wrap my head around it. I guess an English speaker has to broaden our horizons a little. If we can say: "I can swim/dance/sing..." without a requisite "know how to", we should get more comfortable with the phrase in other languages. And really, in this context, we were already talking about speaking languages, so the "snakke" shouldn't be necessary.
Just out of curiosity, would a Norwegian speaking both nynorsk and bokmål (but only those two languages) be considered bilingual since nynorsk and bokmål are two Norwegian languages, or would that person still be considered monolingual, since both nynorsk and bokmål are forms of Norwegian?