Check with an attorney in your area... Some "letters of intent" are binding agreements depending on terms specified in the letter: work, hours, scope of work, etc... Just because the other party did not sign the agreement does not make it non-binding per se. Once you begin work, there is an implied agreement that the other party accepted those terms and you may have accepted some you don't know about.
Be careful with letters of intent as the sole means of initiating an agreement.
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