And in the Spanish word mañana ("tomorrow" or "morning'), the ñ is actually very close to a "soft н" in Russian, while the n is close to a "hard н".
I'm smacking myself on the forehead because I overlooked a native English example -- the difference (in some dialects of English) between "do" and "dew", or between the initial sounds of "tool" and "tulip".

And the reason I overlooked this example is that in my own dialect of US English, I pronounce "do" and "dew" identically, and the "t" sounds in "tool" and "tulip" are also the same for me. But for other English speakers, the initial sounds in "do" and "tool" are similar to the hard д and т in Russian, while the initial sounds in "dew" and "tulip" are similar to the soft Russian consonants.