@engineer,
												Thanks, Engineer!
Aha, so it's 'so as to not' instead of 'so as not to'. 
Since 'I'm not so sick as to not work' doesn't have the 'can/be able to' element,  unless you go with:
 'I'm not so sick as to not be able to work today' 
which is kinda long, you prefer:
'I'm not so sick that I can't work' ... Right?