Surface Area and Volume · Hard problem

Two rectangular boxes are pushed together to form an L-shaped block: Box A is $6$ cm by $4$ cm by $3$ cm, and Box B is $3$ cm by $4$ cm by $5$ cm, joined so that a $3$ cm by $4$ cm face of each is glued fully together. What is the total surface area of the L-shaped block, in square centimeters?