Now isn't that an interesting paradox of language usage !6500k is hotter than 5000k yet is described as being cooler
Abaazov, learn softproofing, play around with the rendering intents and make adjustments to the image with proof colors ticked. You'll notice a difference but I don't think it will cure the problem of the prints being too dark. There is a 'kludge' fix to this problem, however, if the brighter lighting doesn't work.
After making a print, adjust the image on the monitor so that it looks as dark as the print. Next time you print (and for all subsequent prints), make the reverse adjustments to the image just before printing. (ie. if the darkening adjustment involved moving the gamma slider in levels to say 0.8, then move it the other way to 1.2). The image on the screen will then look too light, but should print right. It sort of defeats the purpose of calibration, but if it's just a lightness/darkness issue and the colors are okay, it might work.