Hi Timdeg, a hydrometer wont read 1.000 in water, so it cannot be tested that way, unusual readings may have an explanation though. The OG sounds too low - it may be that all the sugars in the malt had not fully dissolved so the reading was lower than expected.
If after 11 days the current gravity reading is 1.006 then this is good and well below the 1.011 you are aiming for, so as long as it is constant now the brew can be bottled or barrelled.
If the reading is 1.060 then this would indicate it still has along way to go, just check it is warm enough, at least 20 degrees C for most brews, maybe give it a good stir to re-suspend the yeast, and if the reading wont lower then it will need a new yeast to get it going.
Here's a helpful link to a ABV calculator. The site it links to is an interesting blog.
http://www.brewersfriend.com/abv-calculator/