This is governed not by the brokerage but by the exchange, specifically the "opening rotation" procedure. If there is a sell (limit) order at $10 and a buy order at $11 going into the open, the first trade would probably be designated at the midpoint ($10.50) for the lesser of the two quantities. But it is unlikely that these would be the only orders.
More typically, in an active stock, a spectrum of orders will pin down the opening price based on clearing the market. A hypothetical opening price of $X would involve executing all sell orders below $X (total shares an increasing function of X) and all buy orders above $X (total shares a decreasing function of X), along with any or all of the orders at exactly $X. Up to the price granularity at which orders are typically spaced, there will be a unique price (solution for X) at which an equal number of shares is bought and sold, and this is how the exchange determines the opening price.
If all buy orders are below all sell orders at the open, the security may not have an "opening price" at all (unless a market maker is required to produce one). The orders would simply initialize the day's order book, and any trades would occur if and when someone hits the evolving bid or ask. In the extreme, daily volume might be zero (as with many options).
EDIT: See here for the NYSE opening procedure. On this exchange, the opening price $X is the one where the maximum number of shares can be traded -- effectively equivalent to the supply-demand balancing described above. Ties are resolved by keeping as close as possible to a reference price (rather than a midpoint rule). Specific examples are given with "crossed" orders (buy above sell) as well as other scenarios.