No, you do not need to file taxes if your only income is from SSDI and Long Term Disability.
You can check out the TurboTax FAQ below for more information about the taxability of Disability:
https://ttlc.intuit.com/replies/3301926
"No, you do not need to file taxes if your only income is from SSDI and Long Term Disability."That may not be a correct statement, as some types of LTD are taxable/