Flaky tests are tests that pass or fail nondeterministically on the same version of code. These tests can mislead developers concerning the quality of their code changes during regression testing. A common kind of flaky tests are order-dependent tests, whose pass/fail outcomes depend on the test order in which they are run. Such tests have different outcomes because other tests running before them pollute shared state. Prior work has proposed repairing order-dependent tests by searching for existing tests, known as "cleaners", that reset the shared state, allowing the order-dependent test to pass when run after a polluted shared state. The code within a cleaner represents a patch to repair the order-dependent test. However, this technique requires cleaners to already exist in the test suite. We propose ODRepair, an automated technique to repair order-dependent tests even without existing cleaners. The idea is to first determine the exact polluted shared state that results in the order-dependent test to fail and then generate code that can modify and reset the shared state so that the order-dependent test can pass. We focus on shared state through internal heap memory, in particular shared state reachable from static fields. Once we know which static field leads to the pollution, we search for reset-methods in the codebase that can potentially access and modify state reachable from that static field. We then apply an automatic test-generation tool to generate method-call sequences, targeting these reset-methods. Our evaluation on 327 order-dependent tests from a publicly available dataset shows that ODRepair automatically identifies the polluted static field for 181 tests, and it can generate patches for 141 of these tests. Compared against state-of-the-art iFixFlakies, ODRepair can generate patches for 24 tests that iFixFlakies cannot.