Now that you can play Major Sixth voicings in your left hand, let's take them a step further with a cool modernistic sound.
First, practice this voicing in all 12 keys (just raise the notes by half steps using the same fingerings):
C F Bb (1 2 4 fingering)
-- Start in the fourth octave. ex. C F Bb, then C# F# B, then D G C, etc. etc.
Next, play a major sixth voicing in your left hand (third octave), then play a fourth voicing (like you just learned) off of the major third.
LH: C E G A RH: E A D
Simply take this voicing and practice it in all 12 keys by raising the voicing by half steps.
Once you have them down solidly, you can practice fourths off of the seventh:
LH: C E G A RH: B E A
Practice playing these voicing in order (raising them by half steps), then playing them randomly on the spot.
In order to do so, all you need to know are your fourth LH M6 voicings and fourth voicings in all keys... Play the fourth voicing off of the major third -- and there you have a modernistic sounding major chord consisting of the thirteenth and 9th on top!