@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?