Here is a playthrough of the sixth world. It is split into two parts and it is unedited, but to save you some time (unless you want the entertainment), use the time links in the description of the video and feel free to mute the video.
If you get stuck on the randomly generated puzzles or the puzzle race at the end, just keep at it until you get it! They sometimes are the reason my videos are split because I had to take a break. They can take awhile. If you are on the first puzzle, feel free to restart if you aren't comfortable with the level.
Levels 6-1 to 6:12:
Levels 6-13 to 6-30: