A couple of follow up questions:
1.) as the poster above says, the recipe would help. Sometimes it is difficult for yeast to metabolize the some of the sugars in extract syrups that haven't been fully converted to consumable monosaccharides.
2.) Just a thought: did you add your extract to your water when your heat source was fired? That can cause carmelization (maillard reaction) of the sugars in the extract syrups and complicate/prevent the yeast's metabolization of them.
3.) You absolutely, unequivocally need a hydrometer and some sort of sample thief to pull samples (a santized, decent-sized turkey baster will work in a pinch). Otherwise, you have no way of knowing if the beer is finished.
4.) As the above poster said, I have learned to leave brews in the primary for a minimum of 2-3 weeks, usually no more than 4. Even when those beautiful, smile-inducing airlock bubbles stop, the yeast is still working to make your beer better, primarily by cleaning up some other waste products, including, but not limited to diacetyl. 6 days is not a long time.
5.) Is the beer undrinkable (loaded question)? My first brew (imperial blonde) was a tad on the sweeter side, but both my fiancee and I loved drinking it. If its ok but not your favorite, I would keep it around, and it could mature some more in the bottles. It is still a pretty 'green' beer and would benefit from some additional maturation.
Here's my best suggestion:
If this beer is in the bottles, not a whole lot you can do without some major brain damage, equipment and risk of infection. I know you probably have the itch to brew about 10 different styles at this point, but I would buy the exact same kit (and a hydrometer), exact same brewday practices, but this time leave it in the primary for 21 days then rack/prime/bottle. In 5-6 weeks, you can taste the two side by side and taste the difference. If you really need to get another style under your belt, buy another ale pail and another kit. IMHO, you (and your palette) have the opportunity to learn an invaluable lesson from this experience.
Let us know how it turns out!