I would like to point out, that the 5760 dots from a printer are not directly corresponding to the resolution of a printer in terms of ppi. Actually a number of such dots are used to display one pixel.
Epson printers, for example, have a native resolution of 360 and 720 ppi (Canon has 300 and 600), and this is realized with 5760 dpi print head.
Theoretically correct, but most printer drivers derive their start point from the ppi resolution value.
If sending to an Epson printer, the initial output resolution from the likes of Lightrooms print module needs to be set to 360 or 720 to avoid possible artifacts in the print. In other words, the final print head resolution needs to be equally divisible by the initial output resolution - again, something else that a lot of people get wrong.
I would assume that a printer (or the printer driver) does more than just stupidly repeating dots until meets the pixel dimension, but uses the printerâs capability of applying droplets of various sizes.
The reason why it is better to enter the native printer resolution in Lightroomâs printing module is simply that the scaling algorithms of e.g. Lightroom (or QImage, which I use) are more intelligent than the rather simple ones in the drivers.
BTW, the âppiâ term is actually correct in the printer dialogs - it describes how many of the imageâs pixels will ultimately land on one inch of paper. They get there by the printer intelligently spraying dots (droplets) of various sizes and colors for each pixel. Thatâs why the dpi capability of a printer is much higher than e.g. the native printer resolution, be it 360 for Epson or 300 for Canon. At least thatâs my understanding.
I have to say my experience, of printing large (A0) and the many working days becoming working nights and on to many occasions working days again without rest because the print just doesnât come out right before a deadline, tells me that itâs indeed jedi stuff 
That was generally more complex content than a simple photo though.