Cook linguine in large pot of boiling salted water until al dente about 10 minutes, stirring occasionally. Drain pasta and return to same pot to keep warm. Mix in 1 tablespoon butter.
Heat oil in heavy large skillet over medium heat. Add shrimp and sauté until just cooked through, stirring frequently, about 3 minutes. Using slotted spoon, transfer shrimp to bowl. Add garlic, shallots and 1 tablespoon butter to skillet. Cook 2 minutes. Add clam juice and wine. Increase heat and boil until mixture is reduced by half, about 8 minutes. Whisk in remaining 5 tablespoons butter. Return shrimp and any accumulated juices to skillet. Add parsley, dill, pepper and pasta and toss to blend well. Season to taste with salt.