Well, it seems that atom counts are okay, but you've forgotten ionic counts. This is why redox reactions are hard to study.
You said that this redox should be in basic solution; so just put OH-
ions to the left side. However, there is a serious error; in basic solutions, permanganate is only reduced to manganese dioxide, as you correctly wrote. So the coefficients cancel to reflect this:
So if we write its real forms, we'll get this one:
[tex]NO + KMnO_4 \longrightarrow KNO_3 + MnO_2 [/tex]