Any question of law or fact arising in regard to the application of the plan in determining the compensation payable thereunder or otherwise shall be determined either by agreement or by arbitration, or by an action at law as herein provided. In case the employer shall be in default in any of his obligations to the employee under the plan, the injured employee or his committee, conservator or guardian, if such be appointed, or his executor or administrator, may then bring an action to recover compensation under the plan in any court having jurisdiction thereof as on a written contract. Such action shall be conducted in the same manner as an action at law for the recovery of damages for breach of a written contract, and shall for all purposes, including the determination of jurisdiction, be deemed such an action. The judgment in such action, in favor of the plaintiff, shall be for a lump sum equal to the amount of the payments then due and prospectively due under the plan. In such action by an executor or administrator the judgment may provide the proportions of the award or the costs to be distributed to or between the several dependents. If such determination is not made it shall be determined by the surrogate’s court by which such executor or administrator is appointed, in accordance with the terms of this article on petition of any party on such notice as such court may direct.