The melodic minor scale is a scale that can take on a whole new life when applied to jazz. This scale is a very useful and versatile scale for improvisers to know and not just for soloing over minor chords or tonalities. The melodic minor presents some nice harmonic options when you are looking to get away from just playing diatonically over common chord progressions in your solos.
You can even utilize the melodic minor scale over major 7, minor 7b5 and dominant 7 and altered dominant 7th chords. It really is a fundamental substitution method in jazz, so there are many applications from learning just this one scale.
There are four ways (in C minor) to use the melodic minor scale over different chords in your solos (In addition to the C minor). You can use the 3rd,4th, 6th and 7th degrees to produce the modes useful to jazz substitutions. See below:
Here are the fingerings for a the CMAR (Cry Me a River) lick.