The person against whom a jeopardy determination is made may petition for the redetermination thereof pursuant to Article 5 (commencing with Section 60350). That person shall, however, file the petition for redetermination with the board within 10 days after the service upon that person of notice of the determination. At the time of filing the petition for redetermination, the person shall deposit with the board that security as the board may deem necessary to ensure compliance with this part.