I work in the public sector and contribute $18k into a 457(b) plan. I also work in the private sector and contribute $18k into a 401(k) plan. Can I claim both deductions?

I have two jobs (public and private sector) and contribute the full $18k into both plans in the same tax year,  I want to know if I can claim both tax deductions in the same tax year (i.e. $36k of retirement plan deductions).